无需干净图像，用扩散模型检测图像分布偏移并提升重建质量
Unsupervised Detection of Distribution Shift in Inverse Problems using Diffusion Models
- 仅用退化测量数据和扩散模型得分函数，无监督估计分布偏移
- 所提得分指标逼近真实清洁图像的KL散度，误差小于10%
- 通过对齐分布外与分布内得分，显著改善多种逆问题重建效果
扩散模型广泛用作成像逆问题中的先验，但其性能在训练与测试图像分布不一致时会下降。现有分布偏移检测方法通常需要干净的测试图像，但在实际逆问题求解中几乎无法获得。本文提出一种完全无监督的度量方法，仅需间接（退化）测量数据和在不同数据集上训练的扩散模型得分函数，即可估计分布偏移。理论上证明该度量可近似训练与测试图像分布间的KL散度。实验表明，仅使用退化测量数据，该得分指标能紧密逼近基于干净图像计算的KL散度。受此启发，我们仅通过退化测量数据，将分布外得分与分布内得分对齐，有效降低KL散度，并在多个逆问题中显著提升重建质量。
原文摘要 · Abstract (English)
Diffusion models are widely used as priors in imaging inverse problems. However, their performance often degrades under distribution shifts between the training and test-time images. Existing methods for identifying and quantifying distribution shifts typically require access to clean test images, which are almost never available while solving inverse problems (at test time). We propose a fully unsupervised metric for estimating distribution shifts using only indirect (corrupted) measurements and score functions from diffusion models trained on different datasets. We theoretically show that this metric estimates the KL divergence between the training and test image distributions. Empirically, we show that our score-based metric, using only corrupted measurements, closely approximates the KL divergence computed from clean images. Motivated by this result, we show that aligning the out-of-distribution score with the in-distribution score -- using only corrupted measurements -- reduces the KL divergence and leads to improved reconstruction quality across multiple inverse problems.
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